Evaluate the product \[ (a-10) \cdot (a-9) \cdot \dotsm \cdot (a-1) \cdot a, \] where $a=2$.
Note that $a-2 = 0$, since $a = 2$.  Thus the product in question is \[ (a -10) \dotsm (a-3) \cdot (a-2) \cdot (a-1) \cdot a = (a-10) \dotsm (a-3) \cdot 0 \cdot (a-1) \cdot a, \] which is $\boxed{0}$, since zero times any real number is zero.